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IET Cyber-Systems and Robotics
IET Cyber-Systems and Robotics
    
高效网格形变的线性几何代数转子估计器
Jin Wu1, Mauricio Lopez2, Ming Liu1, Yilong Zhu1
1Department of Electronic and Computer Engineering, Hong Kong University of Science and Technology, Hong Kong, People's Republic of China 2Buenos Aires Computer Corporation, Buenos Aires, Argentina
Linear geometric algebra rotor estimator for efficient mesh deformation
Jin Wu1, Mauricio Lopez2, Ming Liu1, Yilong Zhu1
1Department of Electronic and Computer Engineering, Hong Kong University of Science and Technology, Hong Kong, People's Republic of China 2Buenos Aires Computer Corporation, Buenos Aires, Argentina
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摘要： 作者解决了两组对应向量（也称为Wahba问题或点云配准）的最佳旋转估计问题。所提出的方法是近年来文献中最快的方法之一，而且它比大多数其他方法具有更强的抗噪能力，准确度和简便性。它是基于求解由欧几里德几何代数中的问题公式导出的线性方程组。作者展示了其在两个应用中的高效性：一是尽可能刚性的（ARAP）表面建模，二是更平滑的旋转增强型ARAP网格动画，后者是唯一一个能够使表面具有四面体模型质量的方法。网格形变是游戏、自动化建造和机器人技术中的关键技术。ARAP技术及其改进的变体虽然已经得到了广泛的研究，但仍然不能高效地实现。本文提出的基于线性几何代数的转子求解方法，为这个核心问题的研究提供了另一个视角。这不仅提高了三维网格形变的真实性能，而且为解决Wahba问题和点云配准问题提供了一种全新的高效解决方案，这与自动化科学和工程有着密切的关系。
Abstract: The authors solve the problem of estimating the best rotation aligning two sets of corresponding vectors (also known as Wahba's problem or point cloud registration). The proposed method is among the fastest methods reported in recent literatures, moreover it is robust to noise, accurate and simpler than most other methods. It is based on solving the linear equations derived from the formulation of the problem in Euclidean Geometric Algebra. The authors show its efficiency in two applications: the as-rigid-as-possible (ARAP) surface modelling and the more smooth rotation enhanced ARAP mesh animation which is the only method capable of deforming surface modes with quality of tetrahedral models. Mesh deformation is a key technique in games, automated construction and robotics. The ARAP technique along with its improved variants, although have been extensively studied, can still not be achieved efficiently. Linear geometric algebra based rotor solution proposed in this study gives another perspective of the kernel problem. This, however, not only improves the real performance of the three-dimensional mesh deformation, but also provides a brand new computationally efficient solution to the Wahba's problem and point cloud registration, which has been closely related to the automation science and engineering.
收稿日期: 2020-04-07
通讯作者: Mauricio Lopez     E-mail: mclopez@outlook.com
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Jin Wu
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引用本文:

Jin Wu, Mauricio Lopez, Ming Liu, Yilong Zhu. Linear geometric algebra rotor estimator for efficient mesh deformation. IET Cyber-Systems and Robotics, 10.1049/iet-csr.2020.0010.

链接本文:

http://www.zjujournals.com/iet-csr/CN/10.1049/iet-csr.2020.0010    或    http://www.zjujournals.com/iet-csr/CN/Y2020/V2/I2/88

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